`exactextractr`

is an R package that quickly and accurately summarizes raster values over polygonal areas, commonly referred to as *zonal statistics*. Unlike most zonal statistics implementations, it handles grid cells that are partially covered by a polygon. Typical performance for real-world applications is orders of magnitude faster than the `raster`

package.

.

Calculations are performed using the C++ `exactextract`

tool. Additional background and a description of the method is available here. Full package reference documentation is available here.

The package provides an `exact_extract`

method that operates analogously to the `extract`

method in the `raster`

package. The snippet below demonstrates the use of this function to compute monthly mean precipitation for each municipality in Brazil.

```
library(raster)
library(sf)
library(exactextractr)
# Pull municipal boundaries for Brazil
brazil <- st_as_sf(getData('GADM', country='BRA', level=2))
# Pull gridded precipitation data
prec <- getData('worldclim', var='prec', res=10)
# Calculate vector of mean December precipitation amount for each municipality
brazil$mean_dec_prec <- exact_extract(prec[[12]], brazil, 'mean')
# Calculate data frame of min and max precipitation for all months
brazil <- cbind(brazil, exact_extract(prec, brazil, c('min', 'max')))
```

`exactextractr`

can summarize raster values using several named operations as well as arbitrary R functions. Where applicable, a named operation will provide better performance and reduced memory usage relative to an equivalent R function. Named operations are specified by providing a character vector with one or more operation names to the `fun`

parameter of `exact_extract`

.

The following summary operations are supported:

Name | Description |
---|---|

`count` |
Sum of all cell coverage fractions. |

`majority` (or `mode` ) |
The raster value with the largest sum of coverage fractions. |

`max` |
Maximum value of cells that intersect the polygon, ignoring coverage fractions. |

`mean` |
Mean value of cells that intersect the polygon, weighted by the fraction of the cell that is covered. |

`median` |
Median value of cells that intersect the polygon, weighted by the fraction of the cell that is covered. |

`quantile` |
Arbitrary quantile value of cells that intersect the polygon, weighted by the fraction of the cell that is covered. |

`min` |
Minimum value of cells that intersect the polygon, ignoring coverage fractions. |

`minority` |
The raster value with the smallest sum of coverage fractions. |

`sum` |
Sum of values of raster cells that intersect the polygon, with each raster value weighted by its coverage fraction. |

`variety` |
The number of distinct raster values in cells wholly or partially covered by the polygon. |

`variance` |
The population variance of cell values, weighted by the fraction of each cell that is covered by the polygon. |

`stdev` |
The population standard deviation of cell values, weighted by the fraction of each cell that is covered by the polygon. |

`coefficient_of_variation` |
The population coefficient of variation of cell values, weighted by the fraction of each cell that is covered by the polygon. |

Two additional summary operations require the use of a second weighting raster, provided in the `weights`

argument to `exact_extract`

:

Name | Description |
---|---|

`weighted_mean` |
Mean defined value of cells that intersect the polygon, weighted by the product of the coverage fraction and the value of a second weighting raster. |

`weighted_sum` |
Sum of defined values of raster cells that intersect the polygon, multiplied by the coverage fraction and the value of a second weighting raster. |

Weighted usage is discussed in more detail below.

Undefined (`NA`

) values are ignored in all of the named summary operations when they occur in the value raster. When they occur in the weighting raster, they cause the result of the summary operation to be `NA`

.

In addition to the summary operations described above, `exact_extract`

can accept an R function to summarize the cells covered by the polygon. Because `exact_extract`

takes into account the fraction of the cell that is covered by the polygon, the summary function must take two arguments: the value of the raster in each cell touched by the polygon, and the fraction of that cell area that is covered by the polygon. (This differs from `raster::extract`

, where the summary function takes the vector of raster values as a single argument and effectively assumes that the coverage fraction is `1.0`

.)

An example of a built-in function with the appropriate signature is `weighted.mean`

. Some examples of custom summary functions are:

```
# Number of cells covered by the polygon (raster values are ignored)
exact_extract(rast, poly, function(values, coverage_fraction)
sum(coverage_fraction))
# Sum of defined raster values within the polygon, accounting for coverage fraction
exact_extract(rast, poly, function(values, coverage_fraction)
sum(values * coverage_fraction, na.rm=TRUE))
# Number of distinct raster values within the polygon (coverage fractions are ignored)
exact_extract(rast, poly, function(values, coverage_fraction)
length(unique(values)))
# Number of distinct raster values in cells more than 10% covered by the polygon
exact_extract(rast, poly, function(values, coverage_fraction)
length(unique(values[coverage_fraction > 0.1])))
```

`exact_extract`

allows for calculation of summary statistics based on multiple raster layers, such as a population-weighted temperature. The weighting raster must use the same coordinate system as the primary raster, and it must use a grid that is compatible with the primary raster. (The resolutions and extents of the rasters need not be the same, but the higher resolution must must be an integer multiple of the lower resolution, and the cell boundaries of both rasters must coincide with cell boundaries in the higher-resolution grid.)

One application of this feature is the calculation of zonal statistics on raster data in geographic coordinates. The previous calculation of mean precipitation amount across Brazilian municipalities assumed that each raster cell covered the same area, which is not correct for rasters in geographic coordinates (latitude/longitude).

We can correct for varying cell areas by creating a weighting raster with the area of each cell in the primary raster using the `area`

function from the `raster`

package.

Performing a weighted summary with the `weighted_mean`

and `weighted_sum`

operations is as simple as providing a weighting `RasterLayer`

or `RasterStack`

to the `weights`

argument of `exact_extract`

.

The area-weighted mean precipitation calculation can be expressed as:

`brazil$mean_dec_prec_weighted <- exact_extract(prec[[12]], brazil, 'weighted_mean', weights = area(prec))`

With the relatively small polygons used in this example, the error introduced by assuming constant cell area is negligible. However, for large polygons that span a wide range of latitudes, this may not be the case.

A weighting raster can also be provided when an R summary function is used. When a weighting raster is provided, the summary function must accept a third argument containing the values of the weighting raster.

An equivalent to the `weighted_mean`

usage above could be written as:

```
brazil$mean_dec_prec_weighted <-
exact_extract(prec[[12]], brazil, function(values, coverage_frac, weights) {
weighted.mean(values, coverage_frac * weights)
}, weights = area(prec))
```

Or, to calculate the area-weighted mean precipitation for all months:

```
brazil <- cbind(brazil,
exact_extract(prec, brazil, function(values, coverage_frac, weights) {
weighted.mean(values, coverage_frac * weights)
},
weights = area(prec),
stack_apply = TRUE))
```

In this example, the `stack_apply`

argument is set to `TRUE`

so that the summary function will be applied to each layer of `prec`

independently. (If `stack_apply = FALSE`

, the summary function will be called with all values of `prec`

in a 12-column data frame.)

A multi-raster summary function can also be written to implement complex behavior that requires that multiple layers in a `RasterStack`

be considered simultaneously.

Here, we compute an area-weighted average temperature by calling `exact_extract`

with a `RasterStack`

of minimum and maximum temperatures, and a `RasterLayer`

, of cell areas.

```
tmin <- getData('worldclim', var = 'tmin', res = 10)
tmax <- getData('worldclim', var = 'tmax', res = 10)
temp <- stack(tmin[[12]], tmax[[12]])
brazil$tavg_dec <- exact_extract(temp, brazil,
function(values, coverage_fraction, weights) {
tavg <- 0.5*(values$tmin12 + values$tmax12)
weighted.mean(tavg, coverage_fraction * weights)
}, weights = area(prec))
```

When `exact_extract`

is called with a `RasterStack`

of values or weights and `stack_apply = FALSE`

(the default), the values or weights from each layer of the `RasterStack`

will be provided to the summary function as a data frame.

In the example above, the summary function is provided with a data frame of values (containing the values for each layer in the `temp`

stack), a vector of coverage fractions, and a vector of weights.

In some cases, it is desirable for a summary function to return multiple values for each input feature. A common application is to summarize the fraction of each polygon that is covered by a given class of a categorical raster. This can be accomplished by writing a summary function that returns a one-row data frame for each input feature. The data frames for each feature will be combined into a single data frame using using `rbind`

or, if it is available, `dplyr::bind_rows`

.

In this example, the mean temperature for each municipality is returned for each altitude category.

```
altitude <- getData('alt', country = 'BRA')
prec_for_altitude <- exact_extract(prec[[12]], brazil, function(prec, frac, alt) {
# ignore cells with unknown altitude
prec <- prec[!is.na(alt)]
frac <- frac[!is.na(alt)]
alt <- alt[!is.na(alt)]
low <- !is.na(alt) & alt < 500
high <- !is.na(alt) & alt >= 500
data.frame(
prec_low_alt = weighted.mean(prec[low], frac[low]),
prec_high_alt = weighted.mean(prec[high], frac[high])
)
}, weights = altitude)
```

`exactextractr`

can rasterize polygons though computation of the coverage fraction in each cell. The `coverage_fraction`

function returns a `RasterLayer`

with values from 0 to 1 indicating the fraction of each cell that is covered by the polygon. Because this function generates a `RasterLayer`

for each feature in the input dataset, it can quickly consume a large amount of memory. Depending on the analysis being performed, it may be advisable to manually loop over the features in the input dataset and combine the generated rasters during each iteration.

An example benchmark using the example data is shown below. The mean execution time for `exactextractr`

was 2.6 seconds, vs 136 for `raster`

. Timing was obtained from execution on an AWS `t2.medium`

instance.

```
microbenchmark(
a <- exact_extract(prec[[12]], brazil, weighted.mean),
b <- extract(prec[[12]], brazil, mean, na.rm=TRUE), times=5)
# Unit: seconds
# expr min lq mean median uq max neval
# a <- exact_extract(...) 2.5674 2.586868 2.626761 2.587283 2.613296 2.778957 5
# b <- extract(...) 136.1710 136.180563 136.741275 136.226435 136.773627 138.354764 5
```

Results from `exactextractr`

are more accurate than other methods because raster pixels that are partially covered by polygons are considered. The significance of partial coverage increases for polygons that are small or irregularly shaped. For the 5500 Brazilian municipalities used in the example, the error introduced by incorrectly handling partial coverage is less than 1% for 88% of municipalities and reaches a maximum of 9%.

Although `exactextractr`

is fast, it may still be slower than the command-line `exactextract`

tool. However, some efficiencies, such as the simultanteous processing of multiple layers in a `RasterStack`

, are only possible in `exactextractr`

.

Installation requires version 3.5 or greater of the GEOS geometry processing library. It is recommended to use the most recent released version (3.8) for best performance. On Windows, GEOS will be downloaded automatically as part of package install. On MacOS, it can be installed using Homebrew (`brew install geos`

). On Linux, it can be installed from system package repositories (`apt-get install libgeos-dev`

on Debian/Ubuntu, or `yum install libgeos-devel`

on CentOS/RedHat.)